A. Appendix A (electronic-only) : Summary of abbreviations and notations

 

CZ:

convective zone

EOS:

equation of state

HR:

Hertzsprung-Russel

IRK:

implicit Runge-Kutta scheme

LMR:

limit between a mixed zone and a radiative zone

MZ:

mixed zone, i.e., a convective zone contingently extended by overshooting

PMS:

pre main-sequence

ZAMS:

zero age main-sequence

POST:

post main-sequence

:

number of shells for internal structure, in the atmosphere; number of chemical species; index of the shell, in the atmosphere where the radius of the star is defined

:

mass fraction in mass unit of, hydrogen, helium and heavy elements

:

abundance for the chemical species # i; mean abundance; vector of chemical species; vector of mean chemical species; initial ratio, in mass, of heavy elements to hydrogen contents

:

Pressure, temperature, radius, luminosity, mass, time, Rosseland optical depth

:

Pressure, temperature, radius, luminosity, mass, Rosseland optical depth at the bottom of the atmosphere and at the shell #i

:

radius, luminosity of the star, Rosseland optical depth at the level taken as the radius of the star

:

effective temperature, pressure, optical depth at the external limit of the atmosphere, symbol for law

:

at present time, mass, radius, luminosity, age and ratio, in mass, of hydrogen to heavy elements for the Sun

:

total and initial mass of the star; external mass loss rate, change of mass due to mass defect

:

variables used in the calculations for pressure, temperature, radius, luminosity, mass or mean molecular weight

:

variables used in the calculations for pressure, temperature, radius, luminosity, mass at the bottom of the atmosphere

:

distribution factors for pressure and mass; maximum changes of the chemical species labeled by i, of gravothermal energy

:

variables of OPAL opacity tabulations; Stefan-Boltzman constant; directions, in mass, taking into account the mass defect

:

gradient operator with respect to the mass, gradient, adiabatic gradient, radiative gradient

:

density, specific entropy, specific internal energy, angular velocity, Brunt-Väisäla frequency, adiabatic exponent

:

Rosseland mean opacity, nuclear energy rate, gravothermal energy, energy of neutrinos, velocity of light, contraction factor

:

variable index for the reconstitution of the atmosphere; derivatives in the upper and lower parts of the atmosphere

:

repartition function, repartition constant, index real, derivatives of the repartition function, weight function

:

repartition function, derivatives of the repartition function, weight function for the shell #i

:

flow, incoming/outcoming flow in a MZ of the chemical species #i

, :

incoming/outcoming flow of angular momentum in a MZ, angular momentum, lost rate of angular momentum, Alfèn radius

:

creation rate of the chemical species #i, jacobian matrix, minimum and maximum eigenvalues of the jacobian matrix

:

vector of diffusion coefficients, total diffusion coefficient, microscopic diffusion coefficient of the chemical species #i with respect to #j, turbulent and mixing diffusion coefficients, velocity of diffusion for the chemical species #i

:

mixing-length parameter or, also, index, gravitational constant, local gravity, total gravity of the star

:

Order of B-splines, j-ith B-spline of order h, order of B-splines for the integration of the quasi-static equilibrium, for the interpolation of the chemical species

:

matrix, coefficients, order and number of steps of the IRK scheme

:

abundances at several levels of the IRK scheme

:

intermediate times, interval between intermediate times, temperature, density at intermediate times in the IRK scheme

:

time step, optimal and new time steps

:

required and estimated accuracy for the integration of chemical composition